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How does a non-linear Schrodinger equation implies non-unitary evolution?

  1. Jul 28, 2012 #1
    Hi,

    I several times heard that one way to describe the collapse of the wave-function is to add non linearities in the Schrodinger equation (I know that this approaches are not convincing but that's not my point), however, I don't see why a non linear SE would imply loss of unitarity? As long as the Hamiltonian is hermitean, or real if you see it as a function of [itex]\psi[/itex] and [itex]\psi^*[/itex], we can derive an equation of probability conservation.
     
  2. jcsd
  3. Jul 28, 2012 #2
    you call, loss of unitarity, to the breakdown of the superposition ?



    ------
    and apart there are non hermitian hamiltonians that are unitary.
    Mostafazadeh, Bender.
     
  4. Jul 30, 2012 #3
    Well, I would call loss of unitarity any loss of unitarity, but as I heard of using non-linearities to describe wave-function collapse, and the breakdown of a superposition is non unitary evolution, I'd say maybe =)
     
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